Algebra and proofAdditional / Further Maths

Evaluating fractional powers

Find the root first, then apply the numerator’s power.

  • Use the denominator of the exponent to choose the root.
  • Raise that result to the numerator’s power.
  • For a negative exponent, take the reciprocal.

Example 1

Root, then power

Simplify the expression.

Example 2

Include a reciprocal

Fully simplify the expression.

Your turn

Question 1

Evaluate exactly.

Check answer
Question 2

Evaluate exactly.

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Question 3

Evaluate exactly.

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Question 4

Evaluate exactly.

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Question 5

Evaluate exactly.

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